Using archival Very Long Baseline Interferometry (VLBI) data for 3114 radio-luminous active galactic nuclei, we searched for binary supermassive black holes using a radio spectral index mapping technique which targets spatially resolved, double radio-emitting nuclei. Only one source was detected as a double nucleus. This result is compared with a cosmological merger rate model and interpreted in terms of (1) implications for post-merger time-scales for centralization of the two black holes, (2) implications for the possibility of ‘stalled’ systems and (3) the relationship of radio activity in nuclei to mergers. Our analysis suggests that binary pair evolution of supermassive black holes (both of masses ≥108 M⊙) spends less than 500 Myr in progression from the merging of galactic stellar cores to within the purported stalling radius for supermassive black hole pairs. The data show no evidence for an excess of stalled binary systems at small separations. We see circumstantial evidence that the relative state of radio emission between paired supermassive black holes is correlated within orbital separations of 2.5 kpc.